Simultaneous and Independent OSNR and Chromatic Dispersion ...

Simultaneous and Independent OSNR and Chromatic Dispersion Monitoring Using Empirical Moments of Asynchronously Sampled Signal Amplitudes Volume 4, Number 5, October 2012 Faisal Nadeem Khan Alan Pak Tao Lau Trevor B. Anderson Jonathan C. Li Chao Lu P. K. A. Wai

DOI: 10.1109/JPHOT.2012.2208265 1943-0655/$31.00 ©2012 IEEE

IEEE Photonics Journal

OSNR and Chromatic Dispersion Monitoring

Simultaneous and Independent OSNR and Chromatic Dispersion Monitoring Using Empirical Moments of Asynchronously Sampled Signal Amplitudes Faisal Nadeem Khan, 1;2 Alan Pak Tao Lau, 2 Trevor B. Anderson, 3 Jonathan C. Li, 4 Chao Lu, 2 and P. K. A. Wai 2 1

School of Electrical and Electronic Engineering, Engineering Campus, Universiti Sains Malaysia, Penang, Malaysia 2 Photonics Research Centre, The Hong Kong Polytechnic University, Kowloon, Hong Kong 3 National ICT Australia, The University of Melbourne, Melbourne, VIC 3010, Australia 4 Department of Electrical and Computer Systems Engineering, Monash University, Clayton, VIC 3800, Australia DOI: 10.1109/JPHOT.2012.2208265 1943-0655/$31.00 Ó2012 IEEE

Manuscript received May 30, 2012; revised July 5, 2012; accepted July 6, 2012. Date of publication July 11, 2012; date of current version July 30, 2012. This work was supported by the Hong Kong Polytechnic University under Project J-BB9L and by the Hong Kong Government General Research Fund under Project PolyU 519910. This work was also supported by the Incentive Grant of the Universiti Sains Malaysia. Corresponding author: F. N. Khan (e-mail: [email protected]).

Abstract: We analytically investigate and derive equations for the empirical moments of asynchronously sampled signal amplitudes as functions of signal power, noise power, and accumulated chromatic dispersion (CD) of a transmission link. The solutions of these equations enable low-cost, simultaneous and independent monitoring of in-band optical signal-to-noise ratio (OSNR) and CD of the fiber link for various modulation formats and data rates. Numerical simulations are performed to validate the proposed technique and the results demonstrate independent OSNR and CD monitoring with good accuracy and large monitoring ranges. The influence of first-order polarization-mode dispersion (PMD) on the accuracy of the proposed monitoring technique is also investigated. Index Terms: Optical performance monitoring (OPM), optical signal-to-noise ratio (OSNR) monitoring, chromatic dispersion monitoring, multi-impairment monitoring, fiber-optic communications, empirical moments, asynchronous sampling.

1. Introduction The emergence of reconfigurable optical networks offers the potentials for increased flexibility, reduced network operation and maintenance costs, and better exploitation of available transmission capacity by enabling features like automatic path provisioning, fault identification and management, and network resources optimization. However, the realization of such potential features demands precise and incessant information about the extent of optical impairments contributed by the network as well as their distribution. Therefore, it is envisaged that optical performance monitoring (OPM) will be indispensable for the efficient operation and management of such complex dynamic optical networks [1]. Optical signal-to-noise ratio is one of the most prominent physical layer parameter that needs to be effectively monitored so as to obtain vital information about the quality of transmission link and enable fault detection and diagnosis. Furthermore, there is an essential need for in-band OSNR monitoring of individual wavelength-division multiplexed (WDM) channels as

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each channel may go across different paths (hence different number of optical amplifiers) due to network reconfigurablity enabled by optical add–drop multiplexers (OADMs) [2]. Fiber chromatic dispersion is another key transmission impairment that degrades the performance of high-speed fiber-optic communication systems and, hence, must be adequately compensated. In reconfigurable optical networks, each WDM channel may accumulate different amounts of CD by traversing different paths with dissimilar lengths, thereby making fixed CD compensation techniques less effective in such scenarios [3], [4]. The problem is further aggravated by the fact that CD also changes dynamically with temperature and other physical effects [5]. Therefore, an effective CD monitoring technique that could provide crucial information for adaptive CD compensation within tight tolerances is mandatory. A plethora of techniques has been proposed in recent years for monitoring in-line CD or in-band OSNR in reconfigurable optical networks [6]. Most of these techniques are data rate and modulation format dependent and often necessitate hardware modifications to enable monitoring for different modulation formats and data rates. It is highly anticipated that future dynamic optical networks will encompass mixed modulation formats as well as different data rates. Furthermore, due to high-speed nature of these networks, the signals will be vulnerable to multiple network impairments simultaneously. All these considerations have paved way for substantial interest in the development of techniques that could accommodate mixed modulation formats at different data rates and also monitor multiple network impairments simultaneously and independently. Monitoring techniques incorporating such beneficial features may facilitate significant reduction in monitoring costs. OPM techniques exploiting the statistical properties of the received signal have recently gained significant attention since they may satisfy many of the aforementioned requirements in a practical setting. These include asynchronous amplitude histogram (AAH)-based techniques [7]–[11], asynchronous delay-tap sampling (DTS) [12]–[17] and two-tap sampling-based techniques [18]. Most of these techniques rely on either constructing histograms or generating scatter plots of the signal samples (acquired through asynchronous sampling), from which certain parameters are extracted that have one-to-one relationship with the impairments such as OSNR, CD, and polarization-mode dispersion (PMD). These one-to-one relationships are then exploited for the calibration-based impairments monitoring. These techniques suffer from some or all of the following drawbacks: 1) The effects of different impairments are often intermingled, thus prohibiting simultaneous and independent monitoring of individual impairments; 2) Limited monitoring ranges. Typical CD monitoring ranges for the aforementioned techniques lie in the range of 0–600 ps/nm for 10 Gsym/s systems and 0–150 ps/nm for 20 Gsym/s systems; 3) The processing and implementation complexity as well as monitoring accuracy are also points of concern for e.g., in case of AAH, the distributions for different signal amplitudes are severely overlapped (since asynchronous sampling lacks timing information) and the separation of individual distributions for the extraction of parameters is an arduous task and may culminate in monitoring inaccuracies. While asynchronous DTS substantially reduces the distributions overlap problems, the tap-delay value needs to be precisely adjusted in accordance with the symbol rates and a slight misadjustment in the tap-delay value may result in large monitoring errors [13]. In [19], we have presented the initial results of a proposed OSNR and CD monitoring technique by analyzing the empirical moments of the asynchronously sampled signal amplitudes and using statistical signal processing. In this contribution, we present detailed mathematical analysis and results for this simultaneous and independent OSNR and CD monitoring technique as well as investigate the effect of first-order PMD on the monitoring accuracy of this technique. In particular, we derive equations for the first three moments as functions of signal power, noise power and fiber CD and show that solving for them enables joint OSNR and CD monitoring with good monitoring accuracies. Unlike AAH and DTS-based schemes, the proposed technique is able to decouple the effects of OSNR and CD, thereby facilitating independent monitoring of these parameters over large dynamic ranges. The CD monitoring ranges demonstrated by our technique are several times larger than the ones reported for the existing techniques [8], [9], [13]–[15], [18]. In terms of processing and implementation complexity, the proposed technique also offers certain benefits: 1) Unlike AAHbased techniques, our scheme does not rely on extraction of parameters from overlapped distributions; 2) In contrast with DTS-based techniques, no tap-delay adjustment is required, thus allowing


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Fig. 1. Low-pass equivalent model of an optical transmission system.

the use of same hardware for monitoring at various data rates. Finally, due to the fact that signal amplitude samples are employed for monitoring purposes and since these samples are acquired through asynchronous sampling (without requiring any clock information), this technique is applicable to multiple modulation formats as well as various data rates.

2. Joint OSNR and CD Monitoring Using Empirical Moments of Asynchronously Sampled Signal Amplitudes Consider a fiber-optic transmission system where the data signals are corrupted by the amplified spontaneous emission (ASE) noise contributed by the in-line optical amplifiers and the fiber CD. For simplicity, other transmission impairments such as PMD and fiber nonlinearity are assumed to be negligible. The low-pass equivalent model of the system is shown in Fig. 1, where d ðt Þ is the transmitted signal, which can be written as d ðt Þ ¼

þ1 X

xk pðt kT Þ

(1)

k ¼1

where xk are the complex information symbols that are independent and identically distributed (i.i.d.) random variables with normalized power E ½jxk j2 ¼ 1, pðt Þ is the pulse shape centered at t ¼ 0 and T is the symbol period. The transmitted signal is linearly distorted by the fiber CD, which can be modeled as a linear and time-invariant (LTI) system with impulse response hf ðtÞ, as shown in Fig. 1, and transfer function Hf ð!Þ ¼ F fhf ðt Þg ¼ expðj2 L!2 =2Þ

(2)

where L is the fiber length, and 2 ¼ 2 D=2c is the group velocity dispersion (GVD) parameter. The distorted optical signal can then be written as gðt Þ ¼ d ðt Þ hf ðt Þ ¼

þ1 X

xk pðt kT Þ hf ðt Þ:

(3)

k ¼1

The ASE noise is collectively modeled by a circularly symmetric additive white Gaussian noise (AWGN) process w ðt Þ. The received optical signal r ðt Þ before the optical bandpass filter can be written as r ðt Þ ¼

þ1 X

xk pðt kT Þ hf ðt Þ þ w ðt Þ:

(4)

k ¼1

The signal at the optical filter output with the impulse response ho ðt Þ can be written as qðt Þ ¼ ¼

þ1 X

xk pðt kT Þ hf ðt Þ ho ðt Þ þ w ðt Þ ho ðt Þ

k ¼1 þ1 X

xk eðt kT Þ þ w ðtÞ ho ðt Þ |fflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflffl} nðt Þ |fflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflffl}

where

eðtÞ ¼ pðt Þ hf ðt Þ ho ðt Þ:

(5)

k ¼1

sðt Þ


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In this formulation, sðt Þ and nðt Þ in (5) are the optical filter outputs of the signal and noise components, respectively. Neglecting the thermal and shot noise generated by the photodetector, the electrical signal iðt Þ at the photodetector output is given by iðt Þ ¼ R jsðt Þ þ nðt Þj2

(6)

where R is the photodiode responsivity and we assume R ¼ 1 for simplicity. Furthermore, we assume in our analysis that the signal field has a single state-of-polarization (SOP) (i.e., x -polarized), whereas the noise exists in both orthogonal SOPs (i.e., x - and y -polarized). Therefore, the complex signal and noise components sðt Þ and nðtÞ in (6) can be written as sðtÞ ¼ sR ðt Þ þ jsI ðt Þ nx ðtÞ ¼ nx ;R ðt Þ þ jnx ;I ðt Þ ny ðt Þ ¼ ny ;R ðt Þ þ jny ;I ðt Þ h i h i h i h i with E nx2;R ðt Þ ¼ E nx2;I ðt Þ ¼ E ny2;R ðtÞ ¼ E ny2;I ðt Þ ¼ 2 :

(7)

At the output of photodetector, the photocurrent iðtÞ can be described as the sum of two contributions, one for each SOP, i.e., 2 2 2 2 2 iðt Þ ¼ jsðtÞ þ nx ðtÞj2 þny ðt Þ ¼ sR ðt Þ þ nx ;R ðt Þ þ sI ðt Þ þ nx ;I ðtÞ þ ny ;R ðt Þ þ ny ;I ðt Þ : (8) For a given symbol sequence f. . . xk 1 ; xk ; xk þ1 . . .g at a given time instant t0 such that T =2 t0 T =2, each of the four terms inside the parentheses in (8) has a Gaussian distribution, and hence, the amplitude samples Y of the photocurrent iðt Þ have a noncentral chi-square ð2 Þ probability density function (pdf) given by [20] fY ðy Þ ¼

pffiffiffi c 1 y ðn2Þ=4 ðc 2 þy Þ=22 y 2 e I n=21 22 c 2

(9)

where I ðx Þ is the -th order modified Bessel function of the first kind. This distribution has two parameters: n, which specifies the number of degrees of freedom (i.e., the number of independent random variables) and hence 4 in our case (one per each quadrature component in each polarization) and the noncentrality parameter c 2 given by c 2 ¼ sR2 ðt0 Þ þ sI2 ðt0 Þ þ 0 þ 0 ¼ jsðt0 Þj2 :

(10)

Without intersymbol interference (ISI), the first three raw moments of the distribution of the samples at a fixed sampling instant t ¼ t0 are given by 1 ðt0 Þ ¼ E ½Y ¼ 42 þ c 2 ¼ 42 þ e 2 ðt0 Þ 2

2

2 2

2

2

3

2

2 3

2

2

(11) 2

4

2 2

4

2 ðt0 Þ ¼ E ½Y ¼ ð4 þ c Þ þ 2 ð4 þ 2c Þ ¼ 24 þ 12 e ðt0 Þ þ e ðt0 Þ 2

2

2

4

2

(12)

2

3 ðt0 Þ ¼ E ½Y ¼ ð4 þ c Þ þ 6 ð4 þ c Þð4 þ 2c Þ þ 8 ð4 þ 3c Þ ¼ 1926 þ 1444 e2 ðt0 Þ þ 242 e4 ðt0 Þ þ e 6 ðt0 Þ:

(13)

With CD-induced ISI, the pulse will be broadened and will overlap with the neighboring pulses and E ½jsðt0 Þj 6¼ e ðt0 Þ for ¼ 2; 4, or 6. In that case, 2 2 3 X þ1 h i (14) xk eðt0 kT Þ 5 1 ðt0 Þ ¼ E ½Y ¼ E 42 þ jsðt0 Þj2 ¼ 42 þ E 4 k ¼1 h i 2 ðt0 Þ ¼ E ½Y 2 ¼ E 244 þ 122 jsðt0 Þj2 þjsðt0 Þj4 2 2 2 3 4 3 X X þ1 þ1 (15) xk eðt0 kT Þ 5 þ E 4 xk eðt0 kT Þ 5 ¼ 244 þ 122 E 4 k ¼1 k ¼1


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h i 3 ðt0 Þ ¼ E ½Y 3 ¼ E 1926 þ 1444 jsðt0 Þj2 þ242 jsðt0 Þj4 þjsðt0 Þj6 2 2 2 3 4 3 X X þ1 þ1 xk eðt0 kT Þ 5 þ 242 E 4 xk eðt0 kT Þ 5 ¼ 1926 þ 1444 E 4 k ¼1 k ¼1 2 3 6 X þL þ E 4 xk eðt0 kT Þ 5: k ¼L

(16)

Finally, the statistics of the asynchronous samples can be modeled by considering that the sampling instant t0 is uniformly distributed in ½T =2; T =2, i.e., ft0 ð Þ ¼

1 T

T =2 T =2:

for

(17)

In this case ZT =2

1 1 ¼ T

1 1 ð Þd ¼ 42 þ T

T =2

ZT =2

1 2 ¼ T

T =2

1 T

T =2

1 3 ¼ T

1 3 ð Þd ¼ 1926 þ1444 T

ZT =2 T =2

1 T

ZT =2 T =2

(18)

0 8 2 91 = þ1